Designing formative assessment lessons for concept development and problem solving

Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn. I describe a design research project in which we integrated formative assessment strategies into lesson materials that focus on developing students’ conceptual understanding and their capacity to tackle non-routine problems. A theoretical framework for assessment task design is presented, together with an analysis of research-based principles for formative assessment lesson design. Particular aspects are highlighted: the roles of pre-assessment, formative feedback questions and sample work for students to critique. While there are some early signs that these lessons provide an effective model for teachers to introduce formative assessment into everyday classroom practice, the materials require a radical shift in the predominant culture within most classrooms

Designing formative assessment lessons for concept development and problem solving

Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn. I describe a design research project in which we integrated formative assessment strategies into lesson materials that focus on developing students’ conceptual understanding and their capacity to tackle non-routine problems. A theoretical framework for assessment task design is presented, together with an analysis of research-based principles for formative assessment lesson design. Particular aspects are highlighted: the roles of pre-assessment, formative feedback questions and sample work for students to critique. While there are some early signs that these lessons provide an effective model for teachers to introduce formative assessment into everyday classroom practice, the materials require a radical shift in the predominant culture within most classrooms

Developing students’ strategies for problem solving in mathematics: the role of pre-designed “sample student work”

This paper describes a design strategy that is intended to foster self and peer assessment and develop students’ ability to compare alternative problem solving strategies in mathematics lessons. This involves giving students, after they themselves have tackled a problem, simulated “sample student work” to discuss and critique. We describe the potential uses of this strategy and the issues that have arisen during trials in both US and UK classrooms. We consider how this approach has the potential to develop metacognitive acts in which students reflect on their own decisions and planning actions during mathematical problem solving

Teachers' attempts to integrate research-based principles into the teaching of numeracy with post-16 learners

This paper describes some outcomes of a nine-month design-based research study into the professional development of 24 numeracy teachers with post-16 learners. The teachers were encouraged to integrate eight research-based teaching principles into their classroom practices as they implemented a set of discussion-based mathematics learning resources. A mixed methods approach was used to evaluate the outcomes, including interviews and classroom observation. The paper examines: teachers’ perceptions of the project; the reasons why they found some pedagogical principles more difficult to incorporate than others and the factors that enabled and impeded their use of the learning resources. In particular it is noted that the principles that teachers considered to be most important were not the ones that they were observed using most effectively. The paper concludes by considering the implications of the research for initial and continuing teacher education

Lesson design for formative assessment

The potential power of formative assessment to enhance student learning is clear from research. This, however, demands a different learning culture and a broader range of teaching approaches than are found in most mathematics classrooms. Earlier efforts to introduce formative assessment for learning have focused on teacher professional development. Here we describe a major project that explores how this change may be stimulated and supported by teaching materials that embody the principles of formative assessment. We describe the design challenges we faced, the previous research and development experience we drew upon, and the principles that directed our designs. We illustrate these elements with examples of the products themselves, some outcomes and lessons learned

Developing student questioning when problem solving: the role of sample student responses

This paper describes intervention resources designed to provide opportunities for student self-regulation, with a particular focus on setting subgoals when problem solving. Each task includes a range of pre-written interrelated “sample student responses” that expose students to multiple perspectives on an unstructured non-routine problem. After students attempt the problem they are given the responses to collaboratively complete, critique and compare. We explore students’ capacity to adopt another person’s (the sample student’s) goals in order to complete a solution, and their capacity, through the use of comparison, to identify worthy criteria when critiquing the completed solutions. We then reflect on how we can make subsequent improvements to the resources

Lesson design for formative assessment

The potential power of formative assessment to enhance student learning is clear from research. This, however, demands a different learning culture and a broader range of teaching approaches than are found in most mathematics classrooms. Earlier efforts to introduce formative assessment for learning have focused on teacher professional development. Here we describe a major project that explores how this change may be stimulated and supported by teaching materials that embody the principles of formative assessment. We describe the design challenges we faced, the previous research and development experience we drew upon, and the principles that directed our designs. We illustrate these elements with examples of the products themselves, some outcomes and lessons learned

Developing students’ strategies for problem solving in mathematics: the role of pre-designed “Sample Student Work”

This paper describes a design strategy that is intended to foster self and peer assessment and develop students’ ability to compare alternative problem solving strategies in mathematics lessons. This involves giving students, after they themselves have tackled a problem, simulated “sample student work” to discuss and critique. We describe the potential uses of this strategy and the issues that have arisen during trials in both US and UK classrooms. We consider how this approach has the potential to develop metacognitive acts in which students reflect on their own decisions and planning actions during mathematical problem solving

Developing student questioning when problem solving: the role of sample student responses

This paper describes intervention resources designed to provide opportunities for student self-regulation, with a particular focus on setting subgoals when problem solving. Each task includes a range of pre-written interrelated “sample student responses” that expose students to multiple perspectives on an unstructured non-routine problem. After students attempt the problem they are given the responses to collaboratively complete, critique and compare. We explore students’ capacity to adopt another person’s (the sample student’s) goals in order to complete a solution, and their capacity, through the use of comparison, to identify worthy criteria when critiquing the completed solutions. We then reflect on how we can make subsequent improvements to the resources